The perimeter of the rectangle is 58. If one side is increased by 5 cm and the other by 3 cm

The perimeter of the rectangle is 58. If one side is increased by 5 cm and the other by 3 cm, then the area of the rectangle will increase by 126 cm2. find the sides of the rectangle.

1. Take the length of the rectangle for x, for the width of the rectangle.

2. (x + 5) is the length of the new rectangle, (y + 3) is the width of the new rectangle.

3. We compose two equations:

2x + 2y = 58; x + y = 29;

(x + 5) (y + 3) – xy = 126; xy + 3x + 5y +15 – xy = 126; 3x + 5y = 111;

Multiplying the first equation by (-5), we get – 5x – 5y = – 145; Add it to the second equation:

– 2x = – 34;

x = 17 cm.

y = 29 – 17 = 12 cm.

Answer: the length of the rectangle is 17 cm, the width is 12 cm.